A Repeated Measurements Approach to $SoH$ Battery Modelling of Cyclic Aged Data in a Laboratory Environment

State of health (SoH) is widely used for battery management, but it is a single scalar and offers limited interpretability. Two batteries with similar SoH can exhibit very different degradation behaviors and the lack of interpretability hinders optimal battery operation. In this paper, we propose IBAM for interpretable battery aging modelling with a neural-assisted physics-based framework. IBAM outputs a 2-D aging fingerprint without extra diagnostic tests and uses only routine logs from the battery management system. The fingerprint offers great interpretability by capturing a battery's curve-wide polarization voltage loss and the tail loss near the end-of-discharge. IBAM first creates a physics-based battery model based on a fractional-order equivalent circuit model, and then extracts per-cycle fingerprints from the model using a two-stage least-squares method. IBAM further anchors fingerprints on the SoH axis with physics-guided regression, where the per-cycle SoH is estimated via a bidirectional gated recurrent unit with customized multi-channel voltage features. Across batteries with short-, medium-, and long-lifespans, IBAM consistently yields the best physics model fidelity at different aging stages, and provides clear interpretations of degradation mechanisms and fingerprint patterns about batteries of different lifespans. The resulting fingerprints support interpretable battery health assessment and can inform battery control choices.

In some fields currently dominated by empirical approaches, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models motivated by quasi-physical thinking contain parameters to be estimated from experimental data. Often the structure of such models yields fully or partially confounded parameters, which are difficult or even impossible to estimate reliably. To preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem we introduce a ridge regression scheme. An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper-parameter at each iteration. The formulae presented require fixed point iteration to solve for the hyper-parameter. Given a suitable starting value, analysis demonstrates convergence is very rapid. The optimal hyper-parameter selection mechanism is incorporated within an efficient regularised iterative generalised least squares mechanism, capable of fitting both heteroscedastic and serially correlated data as required. Simulation confirms the efficacy of the overall method.

Degradation prognosis for lithium-ion cells requires forecasting the state-of-health (SOH) trajectory over future cycles. Existing data-driven approaches can produce trajectory outputs through direct regression, but lack a mechanism to propagate degradation dynamics forward in time. This paper formulates battery degradation prognosis as a world model problem, encoding raw voltage, current, and temperature time-series from each cycle into a latent state and propagating it forward via a learned dynamics transition to produce a future trajectory spanning 80 cycles. To investigate whether electrochemical knowledge improves the learned dynamics, a Single Particle Model (SPM) constraint is incorporated into the training loss. Three configurations are evaluated on the Severson LiFePO4 (LFP) dataset of 138 cells. Iterative rollout halves the trajectory forecast error compared to direct regression from the same encoder. The SPM constraint improves prediction at the degradation knee where the resistance to SOH relationship is most applicable, without changing aggregate accuracy.